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Consumption and Market Incompleteness in a Model of Intertemporal Hedging
Working Paper (2011)
  • Qiang Zhang
Abstract
I study the implications of a consumption and portfolio choice model featuring intermtemporal hedging for the relationships between market incompleteness and the optimal consumption, the expected instantaneous consumption growth, and welfare. The model is adapted from Campbell, Chacko, Rodriguez, and Viceira's
(2004) continuous-time formulation of the Campbell and Viceira (1999) setup. The
market incompleteness is indexed by rho; the instantaneous correlation of the expected return and the instantaneous return to the risky asset. The degree of market incompleteness has no direct level effect on consumption when either consumption or portfolio choice is rationally myopic. For these two cases, market incompleteness only a¤ects the level of consumption indirectly through wealth (for both types of rational myopicness) or the expected risky return (for rational myopicness in portfolio choice), though for empirically relevant parameter values these indirect effects are quantitively negligible, especially when rho is non-positive.
In contrast, when a consumer is rationally forward-looking in both consumption and portfolio decisions, market incompleteness directly impinges on consumption level in a complex nonlinear fashion. On the other hand, regardless of how forward-looking a consumer is, market incompleteness does have a direct growth effect, in the sense that the expected consumption growth explicitly depends on the incompleteness parameter: it declines for rho values close to -1, but mostly increases with it afterwards. And the growth effect of rho becomes increasingly more nonlinear, when moving from rationally myopic portfolio choice to rationally myopic consumption decision, to fully rational forward-looking in both decisions.
Keywords
  • Consumption,
  • Market Incompleteness,
  • Intertemporal Hedging
Publication Date
July, 2011
Citation Information
Qiang Zhang. "Consumption and Market Incompleteness in a Model of Intertemporal Hedging" Working Paper (2011)
Available at: http://works.bepress.com/qiang_zhang/7/